An old table in a furniture store is marked down by 10% from its previous price on five separate occasions. What is the total percentage reduction in price correct to two decimal places
What is
1 - (.9)^5 ?
To find the total percentage reduction in price, we need to calculate the cumulative effect of the individual markdowns.
Let's assume the original price of the table is $100.
The first markdown of 10% reduces the price by $100 * 10% = $10. The new price after the first markdown is $100 - $10 = $90.
The second markdown of 10% is applied to the new price, $90. This reduces the price by $90 * 10% = $9. The new price after the second markdown is $90 - $9 = $81.
The third markdown of 10% is applied to the new price, $81. This reduces the price by $81 * 10% = $8.10. The new price after the third markdown is $81 - $8.10 = $72.90.
The fourth markdown of 10% is applied to the new price, $72.90. This reduces the price by $72.90 * 10% = $7.29. The new price after the fourth markdown is $72.90 - $7.29 = $65.61.
The fifth markdown of 10% is applied to the new price, $65.61. This reduces the price by $65.61 * 10% = $6.56. The final price after the fifth markdown is $65.61 - $6.56 = $59.05.
To calculate the total percentage reduction, we compare the final price ($59.05) to the original price ($100) and find the difference: $100 - $59.05 = $40.95.
To express this reduction as a percentage, we divide the difference by the original price and multiply by 100: ($40.95 / $100) * 100 ≈ 40.95%.
Therefore, the total percentage reduction in price, correct to two decimal places, is approximately 40.95%.
To find the total percentage reduction in price, we need to calculate the compounded reduction from each 10% markdown.
To do this, we'll start by calculating the reduction from the first markdown of 10%. We can easily find this by subtracting 10% from 100% (the original price):
100% - 10% = 90%
Now, for the second markdown, we'll need to take the 90% (the price after the first markdown) and calculate a 10% reduction again:
90% - (10% of 90%) = 90% - (10% × 90%) = 90% - 0.1 × 90% = 90% - 9% = 81%
For the third markdown:
81% - (10% of 81%) = 81% - (10% × 81%) = 81% - 0.1 × 81% = 81% - (0.1 × 0.81) = 81% - 8.1% = 72.9%
We will continue this calculation for the remaining two markdowns:
72.9% - (10% of 72.9%) = 72.9% - (10% × 72.9%) = 72.9% - (0.1 × 72.9%) = 72.9% - (0.1 × 0.729) = 72.9% - 7.29% = 65.61%
65.61% - (10% of 65.61%) = 65.61% - (10% × 65.61%) = 65.61% - (0.1 × 65.61%) = 65.61% - (0.1 × 0.6561) = 65.61% - 6.561% = 59.049%
Therefore, the total percentage reduction in price, correct to two decimal places, is 59.049%.